Price level at different money supplies (V and Q held fixed)
With velocity and real output held at your inputs, this shows how nominal output (M × V) and the implied price level (MV ÷ Q) scale as the money supply changes. The row matching your money supply is marked. It illustrates the quantity-theory result that, when V and Q are fixed, money growth feeds straight into the price level — a model relationship, not a forecast of actual inflation.
Money supply (M)
Nominal output (M × V)
Price level (MV ÷ Q)
$2,000B
$14,000B
0.70
$3,000B
$21,000B
1.05
$4,000B
$28,000B
1.40
◀ your inputs
$5,000B
$35,000B
1.75
$6,000B
$42,000B
2.10
$8,000B
$56,000B
2.80
Calculated in your browser — the numbers you enter are never sent to our servers.
4,000 x 7 = 28,000 of nominal output, and a price level of 1.4
MV = PY says the money supply times its velocity equals the price level times real output. With M at 4,000 and V at 7, nominal output is 28,000; against real output of 20,000 that implies a price level of 1.4, meaning prices 40% above the base year.
MV = PQ → Nominal GDP = M × V; Price level P = (M × V) / Q
As written it is an accounting identity and cannot be false: total spending measured one way must equal total spending measured the other. It becomes a theory only when assumptions are added about which terms are stable and which adjust — and that is where the disagreement lives.
Hold V and Y fixed and money growth becomes inflation, one for one
The classical quantity theory assumes velocity is stable and real output is determined by productive capacity rather than money. Under those conditions the only term free to move when M rises is P, so a 10% increase in the money supply produces 10% inflation. That is the basis of the claim that inflation is always and everywhere a monetary phenomenon.
Both assumptions are contested. Velocity has been demonstrably unstable in recent decades. And output is not fixed in the short run when there is slack — money growth can raise real output rather than prices when workers and capacity are idle, which is the entire Keynesian objection. The identity holds regardless; the prediction depends on conditions that frequently do not.
Reliable for hyperinflation, unreliable for the last two decades
For sustained high inflation, the relationship is robust and well evidenced: every hyperinflation on record has been accompanied by rapid money creation, usually to finance government deficits, and no hyperinflation has occurred without it. At that scale the theory is close to descriptive.
At moderate rates the short-run link is weak. Japan expanded its monetary base enormously for two decades with persistent deflation; US M2 grew sharply after 2008 with inflation below target for years. In both cases velocity fell far enough to offset the money growth, which the identity accommodates and the simple prediction does not.
Consistent units, and a base year for the price level
Money supply and output must cover the same period, and the price level returned is an index relative to whatever base year the real output figure is stated in. A price level of 1.4 is meaningless without knowing that base, and comparing price levels derived from different bases will mislead.
Velocity is normally derived from the other three rather than observed, so entering it as an input inverts the usual direction. That is fine for exploring the identity — which is what this page is for — but it means the result is a scenario rather than a measurement of any actual economy.
Frequently Asked Questions
What is the equation of exchange?
The equation of exchange is MV = PQ, where M is the money supply, V is velocity, P is the price level, and Q is real output. It states that total spending generated by money (M times V) equals the nominal value of everything bought (P times Q), so it is true by construction once the terms are defined.
How does the quantity theory of money differ from the equation of exchange?
The equation of exchange is an identity that always balances. The quantity theory of money turns it into a theory by adding the assumption that V and Q are roughly stable, which implies that changes in the money supply translate mainly into changes in the price level.
Why does the classical view assume V and Q are stable?
Classical economists argued that velocity depends on slow-moving habits and payment institutions, while real output is pinned down by real resources and technology. If both are stable in the short run, the equation isolates a direct relationship between money and prices.
How does money growth lead to inflation in this framework?
If velocity and real output stay fixed, any increase in the money supply must show up as a higher price level to keep both sides of MV = PQ equal. That is the channel behind the famous claim that sustained inflation is, at root, a monetary phenomenon.
What are the main criticisms of the quantity theory?
The central criticism is that velocity is not constant. It can fall when people hoard money or when interest rates drop, and it can rise when confidence is high. When V moves, money growth no longer maps neatly into inflation, weakening the theory’s predictive power.
What does the price level output represent?
It is the price index implied by your inputs, calculated as nominal output divided by real output. A value of 1.00 would mean nominal and real output coincide at your chosen base; values above 1 indicate that prices have risen relative to that base.
Should I enter nominal or real figures for output?
Enter real output for Q. The calculator generates nominal output internally as M times V, then divides by your real figure to find the price level. Mixing a nominal value into the Q field would distort the implied price level.
Can this calculator predict actual inflation?
No. It demonstrates the mechanics of the equation of exchange under fixed velocity and output. Real inflation depends on shifting velocity, supply shocks, and central bank policy, so treat the output as a teaching illustration rather than a forecast.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
The velocity of money is treated as stable over the period being analysed.
Real output is determined by real factors such as labour, capital, and technology rather than by the money supply.
The equation MV = PQ holds as an exact identity once the four variables are measured consistently.
Where it stops
Velocity is not actually constant; it shifts with interest rates, expectations, and the payments system, which breaks the clean link from money to prices.
The strict classical result that money growth maps one-for-one into inflation only holds when V and Q are fixed, an assumption that rarely matches short-run data.
The implied price level is an index relative to the units you enter, not a published inflation figure, so it should be compared with care to official statistics.
Related Calculators
Velocity of MoneyHow many times each unit of money is spent in a year — nominal output divided by the money supply.
Money MultiplierHow far a reserve injection expands the money supply under fractional reserve banking, from the reserve ratio.
Inflation RateThe inflation rate between two CPI readings, with the index change alongside the percentage.
GDPGross domestic product by the expenditure method (C + I + G + NX) or the income method — wages, rent, interest, profit, taxes and depreciation.
Average Propensity to ConsumeThe share of income spent and the share saved, from spending and income or from a consumption function.
Average Propensity to SaveThe saving rate as a share of disposable income, with the APC and the Harrod–Domar growth arithmetic.
Marginal Propensity to ConsumeThe share of an extra dollar that gets spent, from two observations, with the spending and tax multipliers.
Marginal Propensity to SaveThe share of an extra dollar saved — the leak that caps the multiplier — from two observations or the MPC.
Results are estimates for planning and analysis based on the figures you enter. They are not accounting, tax, or financial advice — verify with your own records and a qualified professional before making decisions.
Sudha, J. (2026, September 12). Quantity Theory of Money Calculator. Calculator Matters. https://calculatormatters.com/economics/quantity-theory-of-money-calculator/
MLA
Sudha, Jay. "Quantity Theory of Money Calculator." Calculator Matters, 12 Sept. 2026, https://calculatormatters.com/economics/quantity-theory-of-money-calculator/.
Part of Macro Models — 33 calculators, with which one answers which question.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified the MV = PY identity in both directions, so the price level returned always reproduces the nominal output the money side implies.
Frequently Asked Questions now show on the page: 8 answers, checked in a page-by-page audit.
What the calculation assumes and where it stops now show on the page.
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